WASHINGTON (Reuters) – A conservative "Tea Party" favorite beat the establishment choice in a Kentucky Republican Senate primary on Tuesday and Democratic Senate incumbents struggled for survival in Pennsylvania and Arkansas on the biggest day of voting so far this year.

Rand Paul, a doctor and son of libertarian Republican Representative Ron Paul, beat Kentucky Secretary of State Trey Grayson for the Republican nomination for an open U.S. Senate seat in a race seen as an early test of the strength of the movement.

Grayson had been the handpicked choice of Senate Republican leader Mitch McConnell, but Paul capitalized on the grass-roots intensity of Tea Party activists who oppose runaway federal spending and favor more limited government.

"We have come to take our government back," Paul, who will face the winner from a field of five Democrats in November, told supporters in Bowling Green, Kentucky. "This Tea Party movement is a message to Washington that we are unhappy and we want things done differently."

Opinion polls have found voters in a sour mood fueled by distrust of Washington and worries that neither party is doing enough to rescue the economy and restrain government spending.

The anti-Washington mood threatens to sweep away many well-known incumbents and put Democratic control of Congress at risk in November, when all 435 House of Representatives seats, 36 of 100 Senate seats and 37 of 50 state governorships are up for election.

Specter, a 30-year Senate veteran and former chairman of the Judiciary Committee, would be the biggest incumbent to go down so far this year if he loses on Tuesday.

PARTY-SWITCHER

He switched from Republican to Democrat last year after calculating that he could not win a Republican primary, but a 20-point lead over Representative Joe Sestak turned into a dead heat as Sestak questioned Specter's party credentials.

Democratic officials have rallied to Specter's aid, and he aired an ad featuring Obama praising him. But even with a primary victory, Specter would face a tough re-election fight in November against Republican Pat Toomey.

With polls closed, only scattered returns were available.

In Arkansas, two-term incumbent Lincoln is in a tough primary race with Lieutenant Governor Bill Halter, who has been backed by labor unions unhappy with Lincoln's failure to support a bill making it easier to organize workplaces.

Lincoln hopes to avert a June 8 run-off that will be necessary if no candidate wins 50 percent of the vote.

During the debate on an overhaul of financial regulations, Lincoln introduced a tough bill to force investment banks to dump their derivatives businesses in what critics called an overture to the left.

Like Specter, Lincoln faces a tough general election campaign even if she beats Halter. Polls show Representative John Boozman, expected to emerge from a crowded Republican primary, currently leads her in a potential November matchup.

Pennsylvania also held a special House election to replace Democrat John Murtha, who died in February. A Republican victory would be a first step in their climb toward reclaiming House control -- they need to gain 41 seats in the 435-seat chamber.

(Additional reporting by Joanne Allen, Editing by Sandra Maler)

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